Spin

[SamBridge]

I'm pretty sure spin just has something to do with the direction of oscillation. So a particle doesn't have to physical spin it just have to "wave" in a certain forwards or backwards manner.

[Mike Smith Cosmos]

I'm pretty sure spin just has something to do with the direction of oscillation. So a particle doesn't have to physical spin it just have to "wave" in a certain forwards or backwards manner.

 

The mathematicians who explain spin seem to have no requirement for a visual model, claiming that some aspects of the universe are not described in any form we know. I personally don't see why we cant say its a little bit like this , a little bit like that, and mainly the other.

 

Having done some model investigation of atom simulated devices, I have come to the conclusion that the electron does indeed exist fairly near to the nucleus, but so as to absorb some form of rotational energy ( angular momentum) the electron moves in a complex motion , best working against an opposite partner electron having an opposite motion. ( all this working in partial arc motion) Thus to some extent there is probably an oscillatory nature of some sort. This is probably anathema to puritan mathematical atomic physics specialists who would prefer to leave it as a value with no model. I shall probably be hacked to death for ever muttering such non (mathematical only) comments, (primarily due to the Copenhagen agreement ( namely to draw a line under the unknown, and shut up and calculate ). I personally feel we should move on .

 

Whether that helps you with your oscillations , I don't know. ?

 

Keep thinking!

Edited January 10, 2013 by Mike Smith Cosmos

[Amaton]

In my layman interest of QM, I've learned that fundamental particles cannot be imagined in any sensible way compared to our macroscopic world. Thus, I highly doubt that spin, a property of such particles, can also be approached in an intuitive respect.

 

From what I've read, the same mathematical formulation can be applied to an atom's nucleus, something less intimidating as far as how we picture it (even whole atoms and molecules). Could someone provide insight on what maybe these kinds of spin would look like?

[SamBridge]

Yeah mathematicians don't need visuals, but the math still needs to have real meaning, otherwise why did they do all that research to find it? Spin is defined as "clockwise" or "counterclockwise", and in those scenarios I've seen that a wave travels upwards or downwards, it's like harmonic motion. Waves can be modeled from a unit circle, so just imagine spin as going up from 2pi or down from 2pi, and that makes sense because in the conservation of spin an electrons have half integer spin, and pi/2 + 3pi/2 = 2pi otherwise known as "0". It's spin in that its mathematically similar to a dot spinning around a unit circle.

Edited January 12, 2013 by SamBridge

[Mike Smith Cosmos]

In my layman interest of QM, I've learned that fundamental particles cannot be imagined in any sensible way compared to our macroscopic world. Thus, I highly doubt that spin, a property of such particles, can also be approached in an intuitive respect.

 

From what I've read, the same mathematical formulation can be applied to an atom's nucleus, something less intimidating as far as how we picture it (even whole atoms and molecules). Could someone provide insight on what maybe these kinds of spin would look like?

 

I think one thing is certain . Nearly all things we come across, particularly in the Galaxies move and often spin. Everything is moving. Not all but most celestial objects are spinning, even if they are synchronized with a parent body. So as things are captured they spin. The smaller the radius becomes the faster it spins. Then there are quantum restrictions. Most things in the universe are currently captured thus spinning.

 

What this results in , like magnetic moments, fields etc deserves our closest scrutiny. Its not a casual phenomenon.

[SamBridge]

 

I think one thing is certain . Nearly all things we come across, particularly in the Galaxies move and often spin. Everything is moving. Not all but most celestial objects are spinning, even if they are synchronized with a parent body. So as things are captured they spin. The smaller the radius becomes the faster it spins. Then there are quantum restrictions. Most things in the universe are currently captured thus spinning.

 

What this results in , like magnetic moments, fields etc deserves our closest scrutiny. Its not a casual phenomenon.

There is something that was recently brought up called a curl. Even if the field doesn't physically rotate, it can still mathematically be oriented in a specific direction somehow, though it is unclear what the mechanism for this actually is. This probably doesn't answer anything, just more math to try and understand.

[Cap'n Refsmmat]

Yeah mathematicians don't need visuals, but the math still needs to have real meaning, otherwise why did they do all that research to find it? Spin is defined as "clockwise" or "counterclockwise", and in those scenarios I've seen that a wave travels upwards or downwards, it's like harmonic motion. Waves can be modeled from a unit circle, so just imagine spin as going up from 2pi or down from 2pi, and that makes sense because in the conservation of spin an electrons have half integer spin, and pi/2 + 3pi/2 = 2pi otherwise known as "0". It's spin in that its mathematically similar to a dot spinning around a unit circle.

This makes no sense in the context of quantum mechanics. Spin has nothing to do with a particle's wavefunction spinning, or unit circles. Spin is intrinsic angular momentum, and its name has nothing to do with how it is modeled (unfortunately).

[SamBridge]

This makes no sense in the context of quantum mechanics. Spin has nothing to do with a particle's wavefunction spinning, or unit circles. Spin is intrinsic angular momentum, and its name has nothing to do with how it is modeled (unfortunately).

I know the term spin isn't actually physical, I thought I said that, or at least emphasized that, but anyway, you can still model spin using mathematical curls can't you? And wave functions are derived from trigonometric functions aren't they? It doesn't have to be related in the specific fashion that I'm saying, but if the equations use any form of sine or cosine, you should be able to relate certain properties of them to the unit circle, There are of course ways to model such quantum phenomena without trigonometric functions, but both Schrodinger's wave descriptions and Heisenberg's matrices were shown to achieve equivalent results. But like myself, many people tend to prefer Schrodinger's methods because unlike Heisenberg's they have a clearer visual representation.

Edited January 23, 2013 by SamBridge

[Cap'n Refsmmat]

Free particle wavefunctions can be trigonometric functions, but, say, hydrogen atom electrons have much more complicated wavefunctions. Curl doesn't enter into it. Spin is represented as vectors (spinors) in a vector space.

[SamBridge]

Free particle wavefunctions can be trigonometric functions, but, say, hydrogen atom electrons have much more complicated wavefunctions. Curl doesn't enter into it. Spin is represented as vectors (spinors) in a vector space.

Ok yeah, I can see even without models of atoms that it becomes hard to visually relate complex trigonometric functions with the unit circle. But still, can't spin in some way be derived from the direction of oscillation of a field? Otherwise our only option is "that's just the way it is".

[Cap'n Refsmmat]

No, that's just the way it is.

 

Incidentally, wavefunctions typically have complex (i.e. imaginary) values.

[SamBridge]

No, that's just the way it is. Incidentally, wavefunctions typically have complex (i.e. imaginary) values.

Hmm, what exactly is the spin derived from? How was it discovered? Scientists couldn't have distinguished it without some specific meaning.

[Cap'n Refsmmat]

You may want to look into the Stern-Gerlach experiment:

 

https://en.wikipedia.org/wiki/Stern-Gerlach_experiment

[SamBridge]

You may want to look into the Stern-Gerlach experiment:

 

https://en.wikipedia.org/wiki/Stern-Gerlach_experiment

It seems like the "spin" is derived from taking the Heisenberg route, no wonder it doesn't have a direct physical meaning, it's just a implied implication of using trigonometric equations to describe trajectories I guess the answer really is "that's just how it works". Although it does in a way seem like if I really investigated it I could in some way relate it to a unit circle or at least visual trigonometric properties, which in a way it has, but not directly for the unit circle. Do you think it is just a coincidence that I can almost perfectly model the truncating by a plane of the polar equation theta=nh(sin2x) it looks nearly perfectly like the highest probability distribution locations in a p orbital? But of course it isn't exactly a coincidence, there are some properties of particles like waves.

I guess what I really want is to see spin pointed out in the Schrodinger version of things while it's happening in some animation, I realize that it will not be in exactly the same form, but there would seem to be some way to calculate it outside of the Heisenberg mathematics as atoms still had the same properties in the experiments done. If I boil it down enough no matter what I will eventually arrive at "that's just how the math works", but I want to see it one step just before that.

Edited January 23, 2013 by SamBridge

[Mike Smith Cosmos]

It seems like the "spin" is derived from taking the Heisenberg route, no wonder it doesn't have a direct physical meaning, it's just a implied implication of using trigonometric equations to describe trajectories I guess the answer really is "that's just how it works". Although it does in a way seem like if I really investigated it I could in some way relate it to a unit circle or at least visual trigonometric properties, which in a way it has, but not directly for the unit circle. Do you think it is just a coincidence that I can almost perfectly model the truncating by a plane of the polar equation theta=nh(sin2x) it looks nearly perfectly like the highest probability distribution locations in a p orbital? But of course it isn't exactly a coincidence, there are some properties of particles like waves.

I guess what I really want is to see spin pointed out in the Schrodinger version of things while it's happening in some animation, I realize that it will not be in exactly the same form, but there would seem to be some way to calculate it outside of the Heisenberg mathematics as atoms still had the same properties in the experiments done. If I boil it down enough no matter what I will eventually arrive at "that's just how the math works", but I want to see it one step just before that.

 

 

The following is slightly speculative , so needs to be read in that context :

 

Surely this series of experiments ( Stern-Gerlach) has distinct looks of magnets orientating. In view of the magnetic moment caused by electric charge rotation or spin. Surely this is yet another example of a certain measure of actual spin being present in electrons. Be it that most atoms have an equal amount of magnetic moment. Some do not , which I understand are the magnetic materials.

 

Perhaps the spin is only partial arc, not complete rotation. More a vibration. As has been voiced by your good self SamBridge. The vibration need only be an up and down, or as I am saying a partial Arc vibration. Extended against Time or distance such a vibration becomes a sinusoidal Wave.

 

The reason for partial arc is because another electron is often present in the same orbital but in equal and opposite direction. ( hence the Tuning fork model ). repulsion Negative to negative .

 

If necessary this paragraph PinK can be moved to speculation as a new Thread .( What causes Magnetism in Atoms )

Edited January 24, 2013 by Mike Smith Cosmos

[SamBridge]

When I was reading an old quantum physics book I actually did come across a description that treated it physically to an extent, it was saying that a particle with a spin of 1/2 would using extra dimensions have to rotate 640 or 720 degrees to make a full revolution compared to a particle with a spin of 1, thouh it could have had something to do with the vector fields more than physical rotation pretty easily. I don't know exactly why that works, but it seems like another thing that could be explained with trigonometry if only there was some direct way to investigate it. When I think about it, I think about doing sin(.5x), which increases the period twice as much,

but I don't know enough to prove that that's what it is, but the notion makes sense, instead of a particle having to travel to 2pi to complete a cycle it has to travel to 4pi, which is the same as 720 degrees.

Edited January 25, 2013 by SamBridge

[MigL]

I'm just going by memory here, so I could be wrong.

 

T he observational evidence for spin ( other than in a Stern-Gerlach experiment ) is a splitting of spectral lines, called Lamb's shift.

It was theorised by Pauli for the exclusion principle, and put on firm theoretical footing by P.A.M. Dirac with his version of SR compliant Quantum Mechanics, the precursor of Quantum Field Theory.

[SamBridge]

I'm just going by memory here, so I could be wrong.

 

T he observational evidence for spin ( other than in a Stern-Gerlach experiment ) is a splitting of spectral lines, called Lamb's shift.

It was theorised by Pauli for the exclusion principle, and put on firm theoretical footing by P.A.M. Dirac with his version of SR compliant Quantum Mechanics, the precursor of Quantum Field Theory.

I don't know if it was spectral lines specifically, but it was calculated by modeling some kind of diffraction and interference of light.

[Mike Smith Cosmos]

It seems like the "spin" is derived from taking the Heisenberg route, no wonder it doesn't have a direct physical meaning, it's just a implied implication of using trigonometric equations to describe trajectories I guess the answer really is "that's just how it works". Although it does in a way seem like if I really investigated it I could in some way relate it to a unit circle or at least visual trigonometric properties, which in a way it has, but not directly for the unit circle. Do you think it is just a coincidence that I can almost perfectly model the truncating by a plane of the polar equation theta=nh(sin2x) it looks nearly perfectly like the highest probability distribution locations in a p orbital? But of course it isn't exactly a coincidence, there are some properties of particles like waves.

I guess what I really want is to see spin pointed out in the Schrodinger version of things while it's happening in some animation, I realize that it will not be in exactly the same form, but there would seem to be some way to calculate it outside of the Heisenberg mathematics as atoms still had the same properties in the experiments done. If I boil it down enough no matter what I will eventually arrive at "that's just how the math works", but I want to see it one step just before that.

 

As a previous comment by yourself , you spoke of a vibration or oscillation. Where a point such as an electron , vibrating or it could be described as oscillating about a mean point. If then for reasons of trying to represent this vibration one extended the displacement from the mean point , against time, one could represent this as a sine wave. Be it that this is merely a representation against time it looks more like we imagine a wave. However the electron at this stage would not be transmitting an electro magnetic wave or it would be expending its energy. This is not possible unless the electron is able to go to a different energy band. However if it is vibrating or oscillating as part of its nature, then it obviously has a wave like nature. ( An oscillation or vibration being part of the electrons nature). All that is needed is for this vibration or oscillation being in some way creating an actual angular momentum. If the electron is present at an orbital radius r then a circular force would be present as . . --mv(squared)/r as v in one direction is -v in the opposite direction ( 2 separate v's in opposite directions ), however v(squared) remains positive. (spin can be 2) then angular momentum is present, but no loss of energy, until a change of orbit. ?

Edited January 28, 2013 by Mike Smith Cosmos

[swansont]

I'm just going by memory here, so I could be wrong.

 

T he observational evidence for spin ( other than in a Stern-Gerlach experiment ) is a splitting of spectral lines, called Lamb's shift.

It was theorised by Pauli for the exclusion principle, and put on firm theoretical footing by P.A.M. Dirac with his version of SR compliant Quantum Mechanics, the precursor of Quantum Field Theory.

 

You may be thinking of the Zeeman shift (or splitting), which occurs in magnetic fields and depends on the spin. The Lamb shift is a difference in energy between the S and P states in Hydrogen, so it's not directly related to spin.

[Amaton]

Where a point such as an electron , vibrating or it could be described as oscillating about a mean point. If then for reasons of trying to represent this vibration one extended the displacement from the mean point , against time, one could represent this as a sine wave.

 

Not the person you replied too, but this really helps. I was aware of the notion that oscillating particles can be modelled rectilinearly (in straight lines), but I couldn't reconcile this with the wave functions which describe them. "Waves" and "straight lines" just wouldn't click in my head. That is until I realized that the function is derived when the oscillation is measured against time. So your explanation just cleared up a lot of confusion, thanks.

[Mike Smith Cosmos]

Not the person you replied too, but this really helps. I was aware of the notion that oscillating particles can be modelled rectilinearly (in straight lines), but I couldn't reconcile this with the wave functions which describe them. "Waves" and "straight lines" just wouldn't click in my head. That is until I realized that the function is derived when the oscillation is measured against time. So your explanation just cleared up a lot of confusion, thanks.

 

I think the whole notion of Sine x at school was a bit mystifying. However when seen as a point , going around a circle extended in time , coming out as a wave , takes all the mystery away.

 

No wonder most things in the Universe are :

 

Either

a ) ROUND

 

b) Going round in a circle

 

c) Spinning

 

or have connotations of

 

d) Waves

[swansont]

But sin(x) is a standing wave, i.e. measured against position, not time. You can have traveling waves, too, where the function at any point changes in amplitude.

 

A circle minimizes the enclosing line, like a sphere minimizes surface area. Nature tends to minimize certain parameters, which, in terms of feedback, is what you'd expect. Oscillations are another feature of feedback, when you have a resonance.

 

It's OK to try and find reasons for such behavior. The issue is what you do with it — declaring victory because you seem to have identified some underlying pattern isn't science. You need to test the rigorously model, and see if it actually works.

[Mike Smith Cosmos]

But sin(x) is a standing wave, i.e. measured against position, not time. You can have traveling waves, too, where the function at any point changes in amplitude.

That was Quick.! I will have to think about that !

 

 

A circle minimizes the enclosing line, like a sphere minimizes surface area. Nature tends to minimize certain parameters, which, in terms of feedback, is what you'd expect. Oscillations are another feature of feedback, when you have a resonance.

 

It's OK to try and find reasons for such behavior. The issue is what you do with it — declaring victory because you seem to have identified some underlying pattern isn't science. You need to test the rigorously model, and see if it actually works.

 

 

How about this sine wave. Generated by a point /electron/ planet going in a circle at so many degrees/second or radians. . The point prescribes a circle. But the situation on a piece of graph paper shows a sine wave being generated.

 

 

 

 

 

 

 

It's OK to try and find reasons for such behavior. The issue is what you do with it — declaring victory because you seem to have identified some underlying pattern isn't science. You need to test the rigorously model, and see if it actually works.

 

 

Not sure what you are getting at here.

 

Surely " declaring victory because you seem to have identified some underlying pattern" is science ( half way house). In other words , one has believed to have made a science related Observation. Thence one can make a postulation, test and possibly verify,or not . Science ( other half ). AS the case may be. No ?

 

Seeing underlying patterns is surely at the cutting edge of new discoveries . No ?

 

Edited April 8, 2013 by Mike Smith Cosmos

[swansont]

How about this sine wave. Generated by a point /electron/ planet going in a circle at so many degrees/second or radians. . The point prescribes a circle. But the situation on a piece of graph paper shows a sine wave being generated.

 

But, like spin (this is a thread on spin, after all), this is not motion-related. Electrons in atoms do not have trajectories. The wave function solutions (more complicated than sinusoids, but still spatially periodic) are stationary states with respect to time.

 

Not sure what you are getting at here.

 

Surely " declaring victory because you seem to have identified some underlying pattern" is science ( half way house). In other words , one has believed to have made a science related Observation. Thence one can make a postulation, test and possibly verify,or not . Science ( other half ). AS the case may be. No ?

 

Seeing underlying patterns is surely at the cutting edge of new discoveries . No ?

 

What I'm getting at is that this is only half of the metaphorical battle. You have this mental model of how it works, but you still need to test that model to be sure. Otherwise you can end up with a model that fails when you try and apply it.